Inverse mass hierarchy of light scalar mesons driven by anomaly-induced flavor breaking

Abstract

We propose a novel mechanism to reproduce the observed mass hierarchy for scalar mesons lighter than 1 GeV (called the inverse hierarchy), regarding them as mesons made of a quark and an anti-quark qq mesons). The source is provided by the SU(3) flavor-symmetry breaking induced by the U(1) axial anomaly. In particular, the anomaly term including the explicit chiral symmetry breaking plays a significant role in the light scalar meson spectrum. To be concrete, we construct a linear sigma model for scalar mesons of qq type together with their pseudoscalar chiral partners, including an anomaly-induced explicit chiral symmetry-breaking term. We find that, due to the proposed mechanism, the inverse hierarchy, i.e., m[a0(980)] = m[f0(980)] < m K∗0 (700)-> m[f0(500)], is indeed realized. Consequently, the quark content of f0 (500)$ is dominated by the isoscalar uu+ dd component, and $f0 (980)$ by the strange quark bilinear one, ss;.